Abstract
Consideration of the normed maps ℝ11 × ℝ11 → ℝ26, motivated by the physical problem of creating a bosonic string from two fermionic strings, leads to the notions of a J3-triple, a J3-supercomplex structure, and J3-hypercomplex equations of two kinds, generalising both the Cauchy-Riemann and Dirac equations in connection with a Clifford—analytipal setting. The problem of constructing all such maps effectively involves the Cayley-Dickson process and the completion method, but up to now only partial results are obtained. The constructions are based upon generalised Hurwitz pairs, their triality and duality.
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Ławrynowicz, J. (1992). The normed maps ℝ11 × ℝ11 → ℝ26 in Hypercomplex Analysis and in Physics. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_43
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DOI: https://doi.org/10.1007/978-94-015-8090-8_43
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